‘sayooza’ (since the emphasis of the word is on the ‘-yoo’, the ‘o’ declines to ‘ah’)
‘savetskikh’ (since the emphasis is on the ‘e’)
‘satsialisticheskikh’ (since the emphasis is on the second ‘i’)
‘respooblik’

You don’t necessarily have to decline the ‘o’, but then it would sound funny if you don’t.
And it is far easier to read the cyrillic word than it is to read a transliterated word as the letters and syllables lose their meaning and pronunciation when the letters are transliterated.